Статті в журналах: "Non linear hydrodynamic"

1

Kalliadasis, Serafim. "Non-linear Mass Transfer and Hydrodynamic Stability." Chemical Engineering Journal 84, no. 3 (December 2001): 608–9. http://dx.doi.org/10.1016/s1385-8947(01)00168-1.

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2

Osipov, A. I., and A. V. Uvarov. "Non-linear hydrodynamic waves in a non-equilibrium gas." Chemical Physics Letters 145, no. 3 (April 1988): 247–50. http://dx.doi.org/10.1016/0009-2614(88)80188-x.

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3

Kristiansen, D., and O. M. Faltinsen. "Non-linear wave-induced motions of cylindrical-shaped floaters of fish farms." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 223, no. 3 (June 12, 2009): 361–75. http://dx.doi.org/10.1243/14750902jeme147.

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This paper addresses the two-dimensional hydrodynamical problem of a floating circular cylinder in waves by means of model tests and numerical simulations. The problem is relevant for floaters of fish farms. Dedicated model tests and computational fluid dynamics (CFD)-simulations, using a presently developed numerical wave tank are presented. Large amplitude sway motion of the cylinder at a wave frequency equal to half the natural sway frequency was observed, both experimentally and numerically. This is argued to be associated with non-linear hydrodynamic effects and instabilities. Further, linear potential flow theory is shown to overpredict the sway motion at resonance of about 500 per cent compared with experiments and simulations. This discrepancy is explained to be mainly attributable to viscous damping caused by flow separation. Higher-order harmonic components of the hydrodynamic forces are significant and should be considered in fatigue life analyses of fish farms.

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4

Ande, Raghu, Stefanie Gutschmidt, and Mathieu Sellier. "Non-linear finite-amplitude oscillations of the large beam arrays oscillating in viscous fluids." Journal of Applied Physics 132, no. 17 (November 7, 2022): 174904. http://dx.doi.org/10.1063/5.0106293.

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Over the past decade, several studies have been conducted on a single and multiple oscillating thin cantilever beams in an unbounded viscous fluid. With an increase in the applications of large array oscillators in a fluid environment for fields like medicine, biology, and energy harvesting devices, it is crucial to understand the nature of the surrounding fluid dynamics. In this present study, we perform a two-dimensional computational fluid dynamics (CFD) analysis of an array of beams oscillating in an unbounded viscous fluid. The two-dimensional Navier Stokes and continuity equations are solved to investigate the hydrodynamic forces exerted on the array members from interaction with the fluid environment. A complex hydrodynamic function is proposed here to represent the distributed hydrodynamic loading experienced by the oscillating beams. Results suggest that there is an increase in viscous damping with an increase in the size of the array. In addition, the nonlinearities become dominant when an array of beams is subjected to large amplitude oscillations. The number of beams in an array determines the overall hydrodynamics and the array effect. CFD analysis can predict the non-linearities unlike boundary integral method (BIM) approach, which is limited for low amplitudes. The results from the full Navier–Stokes simulations compared favorably with results using the BIM for the time-harmonic linearized Stokes equations.

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5

Rajesh, S. R. "Weakly non-linear stability of a hydrodynamic accretion disc." Monthly Notices of the Royal Astronomical Society 414, no. 1 (March 24, 2011): 691–701. http://dx.doi.org/10.1111/j.1365-2966.2011.18435.x.

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6

Sviličić, Šimun, and Smiljko Rudan. "Modelling Manoeuvrability in the Context of Ship Collision Analysis Using Non-Linear FEM." Journal of Marine Science and Engineering 11, no. 3 (February 25, 2023): 497. http://dx.doi.org/10.3390/jmse11030497.

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Ship collisions are rare events that may have a significant impact on the safety of people, ships, and other marine structures, as well as on the environment. Because of this, they are extensively studied but events that just precede collision are often overlooked. To rationally assess collision risks and consequences, a ship’s trajectory, and consequently the velocity and collision angle, should be known. One way to achieve this is through accurate modelling of ship manoeuvrability in collision analysis using non-linear FEM (NFEM). The Abkowitz manoeuvring model is implemented in the LS-Dyna software code and is therefore coupled with FEM calculations. Hydrodynamic forces are calculated in each time step of the LS-Dyna calculation and added to the FE model continuously through calculation. The accuracy of the calculations depends on the choice of and values of hydrodynamic derivatives from the Abkowitz model. Abkowitz’s model derives hydrodynamic forces in the Taylor expansion series to provide hydrodynamic derivatives. The application of the procedure is sensitive on higher-order Taylor series members. This article reviews different sets of hydrodynamic derivatives available for the KVLCC2 ship. Each of them is incorporated into the LS-Dyna NFEM solver by a user-made Fortran subroutine, with standard Zigzag and turning manoeuvres simulated and results compared with the experimental tests. As a result, the optimal selection of hydrodynamic derivatives is determined, laying a foundation for assessing the risk of ship collision due to different ship manoeuvres prior to the collision itself.

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7

Smolec, R. "Survey of non-linear hydrodynamic models of type-II Cepheids." Monthly Notices of the Royal Astronomical Society 456, no. 4 (January 14, 2016): 3475–93. http://dx.doi.org/10.1093/mnras/stv2868.

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8

Moshchuk, N., R. A. Ibrahim, and R. Khasminskii. "Response statistics of ocean structures to non-linear hydrodynamic loading." Journal of Sound and Vibration 184, no. 4 (July 1995): 681–701. http://dx.doi.org/10.1006/jsvi.1995.0341.

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9

Abbasov, A. A., E. M. Abbasov, Sh Z. Ismayilov, and A. A. Suleymanov. "Waterflooding efficiency estimation using capacitance-resistance model with non-linear productivity index." SOCAR Proceedings, no. 3 (September 30, 2021): 45–53. http://dx.doi.org/10.5510/ogp20210300528.

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A modified Capacitive Resistive Model (CRM), with a non-linear Productivity Index (PI), has been suggested to evaluate efficiency of waterflooding in heterogeneous reservoirs. CRM model is based on continuity equation between production and injection, and has several additional advantages. The technique does not require sophisticated geological and hydrodynamics numerical simulation modeling, which would require expensive computing time and based on actual hydrodynamic data. The model adequately describes depletion process and can be used for production forecasting and waterflooding mechanism. Capacitance-resistance model with non-linear productivity index has been tested against numerical model as well as actual production data. Additionally, non-linear productivity index based CRM model was compared against the CRM model with linear productivity index function. The calculations algorithm does not require building static geological models and running dynamic simulations, nor it demands extensive computational resources and time, thanks to using production and injection history only, therefore it can be deployed easily. Keywords: waterflooding; capacitance-resistance model; non-linear productivity index; efficiency; monitoring; forecast.

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10

Dratler, D. I., and W. R. Schowalter. "Dynamic simulation of suspensions of non-Brownian hard spheres." Journal of Fluid Mechanics 325 (October 25, 1996): 53–77. http://dx.doi.org/10.1017/s0022112096008038.

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In this work, we investigate the suitability of models based solely on continuum hydrodynamics for Stokesian Dynamics simulations of sheared suspensions of non-Brownian hard spheres. The suspensions of interest consist of monolayers of uniform rigid spheres subjected to a linear shear field. Areal fractions ranged from ϕa = 0.2 to 0.6. For these suspensions, two sets of Stokesian Dynamics simulations were performed. For the first set, particle interactions were assumed to be strictly hydrodynamic in nature. These simulations are analogous to those of Brady & Bossis (1985) and Chang & Powell (1993). For the second set of simulations, particles were subjected to both hydrodynamic and short-range repulsive forces. The repulsion serves as a qualitative model of non-hydrodynamic effects important when particle separation distances are small. Results from both sets of simulations were found to be within the range of established experimental data for viscosities of suspensions. However, simulations employing the pure hydrodynamic model lead to very small separation distances between particles. These small separations give rise to particle overlaps that could not be eliminated by time-step refinement. The instantaneous number of overlaps increased with density and typically exceeded the number of particles at the highest densities considered. More critically, for very dense suspensions the simulations failed to approach a long-time asymptotic state. For simulations employing a short-range repulsive force, these problems were eliminated. The repulsion had the effect of preventing extremely small separations, thereby eliminating particle overlaps. At high concentrations, viscosities computed using the two methods are significantly different. This suggests that the dynamics of particles near contact have a significant impact on bulk properties. Furthermore, the results suggest that a critical aspect of the physics important at small particle separation distances is missing from the pure hydrodynamic model, making it unusable for computing microstructures of dense suspensions. In contrast, simulations employing a short-range repulsive force appear to produce more realistic microstructures, and can be performed even at very high densities.

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11

Hogg, Michael C., Martin C. Cook, Geoff D. Tansley, and John C. Woodard. "FULL NON-LINEAR STABILITY ANALYSIS OF THE VENTRASSIST HYDRODYNAMIC BEARING SYSTEM." ASAIO Journal 48, no. 2 (March 2002): 140. http://dx.doi.org/10.1097/00002480-200203000-00062.

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12

Wu, G. X. "A note on non-linear hydrodynamic force on a floating body." Applied Ocean Research 22, no. 5 (October 2000): 315–16. http://dx.doi.org/10.1016/s0141-1187(00)00016-x.

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13

Tangasawi, O., S. Theodossiades, H. Rahnejat, and P. Kelly. "Non-linear vibro-impact phenomenon belying transmission idle rattle." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 10 (October 1, 2008): 1909–23. http://dx.doi.org/10.1243/09544062jmes922.

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This paper investigates automotive transmission gear rattle. Specifically, idle gear rattle, where the repetitive impacts of teeth are subject to light loads is investigated. Hydrodynamic regime of lubrication prevails in lightly loaded impact of teeth pairs. Formation of a lubricant film is due to the combined entraining motion of the lubricant and squeeze film effect. A lumped parameter inertial dynamic model, comprising hydrodynamic impact and flank friction for pairs of simultaneous teeth pairs of loose gears is developed. The overall dynamic model includes seven loose gear pairs and rigid body lateral motions of input and output transmission shafts. Therefore, the influence of fluid film behaviour on idle gear rattle is determined, which has hitherto not attracted sufficient research studies. Gear rattle is manifested by a vibration signature, which corresponds to the bands of frequencies due to torsional engine oscillations, meshing frequencies, and impact characteristics of lubricated conjunctions. The spectral contributions are affected by lubricant rheology, specifically its bulk viscosity variation with temperature. It has been found that spectral disposition tends towards lower frequency contributions with reducing lubricant viscosity because of rising temperatures and lowering lubricant stiffness. The findings conform with the experimental results, also reported in the paper. It has also been shown that squeeze film motion plays a significant role in the propensity of transmission system to rattle.

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14

Gammie, C. F., J. Goodman, and G. I. Ogilvie. "Linear and non-linear theory of a parametric instability of hydrodynamic warps in Keplerian discs." Monthly Notices of the Royal Astronomical Society 318, no. 4 (November 11, 2000): 1005–16. http://dx.doi.org/10.1046/j.1365-8711.2000.03669.x.

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15

Chin, C. S., M. W. S. Lau, and E. Low. "Supervisory cascaded controller design: experiment test on a remotely operated vehicle." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 3 (July 29, 2010): 584–603. http://dx.doi.org/10.1243/09544062jmes2223.

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The article proposes a cascaded multi-controllers switching scheme for stabilization and pipeline tracking of a remotely operated vehicle (ROV) under hydrodynamic uncertainties. The ROV is inherently non-linear, highly coupled in motions, and vulnerable to hydrodynamic uncertainties. With controllers that cancel the non-linear dynamics, the system is robust against the pre-defined perturbations on the hydrodynamic added mass and the damping terms. The values used in these perturbed terms were obtained numerically using the WAMITTM software. Compared with other controllers such as proportional-integral and backstepping methods, the pool test showed that the proposed method gives better time domain response and robustness against the perturbed terms.

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16

Abdel-Rahman, Gamal M., and Amal M. Al-Hanaya. "Non-Newtonian Magneto-Hydrodynamic Fluid with Radiation by Stretching Cylinder." Journal of Nanofluids 9, no. 2 (June 1, 2020): 106–13. http://dx.doi.org/10.1166/jon.2020.1738.

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The aim of the present paper is to study the numerical solutions of the steady magnetohydrodynamic and heat generation effects on anon-Newtonian fluid with radiation through a porous medium by a stretching cylinder. The governing continuity, momentum, and energy equations are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically. Numerical results were presented for velocity and temperature profiles for different parameters of the problem are studied graphically. Finally, the effects of related physical parameters on skin friction and the rate of heat transfer are also studied.

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17

Irimiciuc, Stefan-Andrei, Alexandra Saviuc, Florin Tudose-Sandu-Ville, Stefan Toma, Florin Nedeff, Cristina Marcela Rusu, and Maricel Agop. "Non-Linear Behaviors of Transient Periodic Plasma Dynamics in a Multifractal Paradigm." Symmetry 12, no. 8 (August 13, 2020): 1356. http://dx.doi.org/10.3390/sym12081356.

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In a multifractal paradigm of motion, nonlinear behavior of transient periodic plasmas, such as Schrodinger and hydrodynamic-type regimes, at various scale resolutions are represented. In a stationary case of Schrodinger-type regimes, the functionality of “hidden symmetry” of the group SL (2R) is implied though Riccati–Gauge different “synchronization modes” among period plasmas’ structural units. These modes, expressed in the form of period doubling, damped oscillations, quasi-periodicity, intermittences, etc., mimic the various non-linear behaviors of the transient plasma dynamics similar to chaos transitions scenarios. In the hydrodynamic regime, the non-Newtonian behavior of the transient plasma dynamics can be corelated with the viscous tension tensor of the multifractal type. The predictions given by our theoretical model are confronted with experimental data depicting electronic and ionic oscillatory dynamics seen by implementing the Langmuir probe technique on transient plasmas generated by ns-laser ablation of nickel and manganese targets.

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18

Lebed, Igor V. "Derivation of the Multimoment Hydrodynamics Equations for a Gas Mixture." Applied Physics Research 8, no. 4 (July 29, 2016): 103. http://dx.doi.org/10.5539/apr.v8n4p103.

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<p class="1Body">The equations for pair distribution functions are used to derive the multimoment hydrodynamics equations for gas mixture. The gas mixture pair distribution functions are specified. The equations for pair functions are derived directly from the general statistical mechanics concepts. The basic property of the pair functions is established. In conformity with basic property, these functions remain unchanged in time along the trajectory of the center of inertia of a pair. The basic property of the pair distribution functions reveals the existence of an infinite number of principle hydrodynamic values. Multimoment hydrodynamics equations are constructed using 3L+4 principle hydrodynamic values, where is the number of gas mixture components. Just these principle values specify measurable moments. The measurable moments are represented by linear combination of principle and non-principle hydrodynamic values. The general structure of constructed multimoment conservation laws is identical to the structure of appropriate multimoment conservation laws in a gas of identical particles. Each of the multimoment conservation laws is divided into two separate equations. The first group of conservation equations corresponds to convective phenomena. The second group of conservation equations corresponds to dissipative phenomena. Derived multimoment hydrodynamics equations are designed for interpreting the behavior of unstable systems. As is shown previously, classic hydrodynamics equations are incapable of reproducing flows after they lose stability. That is, the solutions to the classic hydrodynamics equations do not find the direction of instability development correctly. The possibility of improvement of classic hydrodynamics equations for a gas mixture is sought on the way toward an increase in the number of principle hydrodynamic values.</p>

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19

Kartal, M. E. "Three-dimensional earthquake analysis of roller-compacted concrete dams." Natural Hazards and Earth System Sciences 12, no. 7 (July 24, 2012): 2369–88. http://dx.doi.org/10.5194/nhess-12-2369-2012.

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Abstract. Ground motion effect on a roller-compacted concrete (RCC) dams in the earthquake zone should be taken into account for the most critical conditions. This study presents three-dimensional earthquake response of a RCC dam considering geometrical non-linearity. Besides, material and connection non-linearity are also taken into consideration in the time-history analyses. Bilinear and multilinear kinematic hardening material models are utilized in the materially non-linear analyses for concrete and foundation rock respectively. The contraction joints inside the dam blocks and dam–foundation–reservoir interaction are modeled by the contact elements. The hydrostatic and hydrodynamic pressures of the reservoir water are modeled with the fluid finite elements based on the Lagrangian approach. The gravity and hydrostatic pressure effects are employed as initial condition before the strong ground motion. In the earthquake analyses, viscous dampers are defined in the finite element model to represent infinite boundary conditions. According to numerical solutions, horizontal displacements increase under hydrodynamic pressure. Besides, those also increase in the materially non-linear analyses of the dam. In addition, while the principle stress components by the hydrodynamic pressure effect the reservoir water, those decrease in the materially non-linear time-history analyses.

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20

Richard, D. "On non-linear hydrodynamic instability and enhanced transport in differentially rotating flows." Astronomy & Astrophysics 408, no. 2 (September 2003): 409–14. http://dx.doi.org/10.1051/0004-6361:20031010.

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21

Trehan, S. K., and R. W. Lardner. "Non-linear standing waves on the surface of a magneto-hydrodynamic jet." International Journal of Engineering Science 27, no. 9 (January 1989): 1107–14. http://dx.doi.org/10.1016/0020-7225(89)90088-8.

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22

Zhang, Lei, Ling Ling Wang, Zhen Zhen Yu, Yuan Bao Leng, Wan Zeng Song, and Bin Zhang. "Characteristics of Non-Linear Internal Waves in a Three-Dimensional Numerical Wave Tank." Applied Mechanics and Materials 212-213 (October 2012): 1123–30. http://dx.doi.org/10.4028/www.scientific.net/amm.212-213.1123.

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Internal waves have a significant impact on the hydrodynamic and stratification characteristics in the density stratified lakes and oceans. In order to reveal the features of internal waves, a three-dimensional numerical wave tank in regular terrain based on the computational fluid dynamics (CFD) model was established to simulate the processes of non-linear internal solitary waves propagation and evolution. The concept of a fraction volume of fluid (VOF) was employed to track the interface of the two-layer fluid. Comparisons were made between CFD model and weakly non-linear KdV theory, it was shown that the wave amplitude predictions by the CFD model agreed well with the KdV equation. On the other hand, the convergence flow and divergence flow at the water surface were captured successfully by the simulated spatial and temporal distributions of velocity. Some peculiar hydrodynamic characteristics, e. g. turbulence kinetic energy and its dissipation rate in the numerical wave tank were also identified and examined. Consequently, this paper provides a reliable method for understanding the phenomenon of internal waves in stratified water bodies.

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23

RUDIN, SERGEY. "NON-LINEAR PLASMA OSCILLATIONS IN SEMICONDUCTOR AND GRAPHENE CHANNELS AND APPLICATION TO THE DETECTION OF TERAHERTZ SIGNALS." International Journal of High Speed Electronics and Systems 20, no. 03 (September 2011): 567–82. http://dx.doi.org/10.1142/s0129156411006866.

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The conduction channel of a semiconductor Field Effect Transistor (FET) or a heterostructure High Electron Mobility Transistor (HEMT) can act as a plasma wave resonator for density oscillations in electron gas, at frequencies significantly higher than the transistor cut-off frequency in a short channel device. The hydrodynamic model predicts a resonance response to electromagnetic radiation at the plasma oscillation frequency. In particular, the hydrodynamic nonlinearities produce a constant source-to-drain voltage when gate-to-channel voltage has a time-harmonic component. In the Dyakonov-Shur detector a short channel HEMT is used for the resonant tunable detection of terahertz radiation. Starting with the quasi-classical Boltzmann equation for a semiconductor and graphene channels, we derived the viscous hydrodynamic model with temperature dependent transport coefficients in both cases. We evaluated the detector response function and in the case of semiconductor channel we also obtained the temperature dependence of the quality factor of the plasma resonance. The present treatment extends the theory of Dyakonov-Shur plasma resonator and detector to account for the temperature dependence of viscosity. In the case of semiconductor channels the treatment here also includes the energy balance equation into the analysis. The numerical results are given in cases of GaAs and GaN channels. We showed that in high mobility semiconductor channels at low temperature the quality of the resonance is strongly limited by the viscosity of the electron fluid. In the case of graphene channel the hydrodynamic model derived here accounts both for electrons and holes, and includes the related diffusion currents. When the gate voltage is a few volts, the Fermi temperature of the electron-hole liquid is considerably higher than the room temperature. In such cases the diffusion currents can be ignored, and from the simplified hydrodynamic equations we evaluated the non-linear response of the plasma in graphene channel to the external perturbation. The results are of interest in potential application to graphene based detectors due to potential of obtaining a channel with the room temperature mobility considerably higher than the mobility in semiconductor channels.

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24

Groves, Mark D. "Theoretical aspects of gravity–capillary waves in non-rectangular channels." Journal of Fluid Mechanics 290 (May 10, 1995): 377–404. http://dx.doi.org/10.1017/s0022112095002552.

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This article reports the results of theoretical research concerning linear waves propagating on the surface of water in a uniform horizontal channel of arbitrary crosssection. Three different versions of the problem are considered. The first is the hydrodynamic problem when surface tension is neglected. The second and third include capillary effects, necessitating the use of edge conditions at the points of contact of the free edges and the channel walls. Two sets of edge constraints are used: pinned edges, where the lines of contact are fixed, and free edges, where the surface meets locally vertical walls orthogonally. These choices are physically realistic and have certain advantages for mathematical analysis.The hydrodynamic problems are shown to have a Hamiltonian structure in which the non-local operators inherent in the water-wave problem are explicitly exhibited. The existence, properties and applications of normal-mode solutions are discussed, and a qualitative comparison of those obtained for each problem is given. Explicit and numerical calculations of the dispersion relations for the normal modes are also carried out. A long-wave theory based upon a decomposition of the hydrodynamic problems in Fourier-transform space is developed. Finally a bifurcation theory for linear travelling waves is discussed, a potential application of which is the construction of an existence theory for periodic travelling-wave solutions of the corresponding nonlinear problems.

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25

Suzuki, Hideyuki, Yuta Sakai, Yasuo Yoshimura, Hidetaka Houtani, Lucas H. S. Carmo, Haruki Yoshimoto, Ken Kamizawa, and Rodolfo T. Gonçalves. "Non-Linear Motion Characteristics of a Shallow Draft Cylindrical Barge Type Floater for a FOWT in Waves." Journal of Marine Science and Engineering 9, no. 1 (January 6, 2021): 56. http://dx.doi.org/10.3390/jmse9010056.

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A shallow draft cylindrical barge type floater with footing close to the water surface was experimentally evaluated in waves to investigate non-linear motion characteristics. The floater was designed to be used as an option for FOWT—floating offshore wind turbines. The non-linear mechanism can be promoted due to the viscous force that acts on the footing edges and the footing interaction with the free surface. In general, the observed non-linear viscous damping is modeled as a force proportional to the square of the relative velocity between the floater and the water. Therefore, the viscous damping levels is expected to increase, and the response in waves, to decrease. However, an increase in motion responses was observed for a broad range of wave periods. An attempt was made to clarify the hydrodynamic mechanism by comparing wave tank experiments, numerical calculations by CFD—computational fluid dynamics codes, and linear potential theory codes. Regular wave tests for three different wave height conditions were carried out, including free decay tests in still waters. For CFD simulations, the OpenFOAM code was selected. For potential theory simulations, the WAMIT code was chosen. As a result of the research, three points could be highlighted and discussed: first, the hydrodynamic phenomenon that contributed to the non-linear motion of the floater was identified; second, the increase and coupling of the motions response of heave and pitch motions; and finally, the phenomenon that the footing held water mass and lifted it to the water surface. The CFD calculations were able to get good qualitative results compared with the experiments and confirmed the use of CFD as a useful tool to capture the non-linear hydrodynamic phenomenon. The linear potential theory was not able to capture the phenomenon discussed herein.

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26

Intartaglia, Carmela, Leonardo Soria, and Maurizio Porfiri. "Hydrodynamic coupling of two sharp-edged beams vibrating in a viscous fluid." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2162 (February 8, 2014): 20130397. http://dx.doi.org/10.1098/rspa.2013.0397.

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In this paper, we study flexural vibrations of two thin beams that are coupled through an otherwise quiescent viscous fluid. While most of the research has focused on isolated beams immersed in placid fluids, inertial and viscous hydrodynamic coupling is ubiquitous across a multitude of engineering and natural systems comprising arrays of flexible structures. In these cases, the distributed hydrodynamic loading experienced by each oscillating structure is not only related to its absolute motion but is also influenced by its relative motion with respect to the neighbouring structures. Here, we focus on linear vibrations of two identical beams for low Knudsen, Keulegan–Carpenter and squeeze numbers. Thus, we describe the fluid flow using unsteady Stokes hydrodynamics and we propose a boundary integral formulation to compute pertinent hydrodynamic functions to study the fluid effect. We validate the proposed theoretical approach through experiments on centimetre-size compliant cantilevers that are subjected to underwater base-excitation. We consider different geometric arrangements, beam interdistances and excitation frequencies to ascertain the model accuracy in terms of the relevant non-dimensional parameters.

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27

Moshchuk, N., and R. A. Ibrahim. "RESPONSE STATISTICS OF OCEAN STRUCTURES TO NON-LINEAR HYDRODYNAMIC LOADING PART II: NON-GAUSSIAN OCEAN WAVES." Journal of Sound and Vibration 191, no. 1 (March 1996): 107–28. http://dx.doi.org/10.1006/jsvi.1996.0109.

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28

Abbasnia, Arash, Mahmoud Ghiasi, and Seyed Mohammad Hossein Sharifi. "Hydrodynamic Modeling Of Fluid Body Interaction By Fully Non-linear Numerical Towing Tank." Journal of Mathematics and Computer Science 04, no. 03 (April 19, 2012): 456–62. http://dx.doi.org/10.22436/jmcs.04.03.20.

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29

Wienkers, A. F., and G. I. Ogilvie. "Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure." Monthly Notices of the Royal Astronomical Society 477, no. 4 (April 14, 2018): 4838–55. http://dx.doi.org/10.1093/mnras/sty899.

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30

Mohapatra, Soumya. "Understanding non-linear hydrodynamic response in heavy-ion collisions via event-plane correlations." Journal of Physics: Conference Series 535 (September 10, 2014): 012033. http://dx.doi.org/10.1088/1742-6596/535/1/012033.

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31

Sharma, Sanjay, and Rajeev Kumar Awasthi. "Performance of Hydrodynamic Journal Bearing Operating under Transient Wear." Mechanics and Mechanical Engineering 22, no. 1 (August 12, 2020): 153–70. http://dx.doi.org/10.2478/mme-2018-0014.

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AbstractThe paper deals with a theoretical study concerning the effect of transient wear on the performance of hydrodynamic journal bearing. The eccentricity ratios are considered 0.3, 0.6 and for varying wear depth from 0.1 to 0.5 for the analysis of purpose. The Reynolds equations governing the flow of lubricant in the clearance space of a hydrodynamic journal bearing system with varying wear depth has been numerically solved using Galerkin’s FEM. The regime is assumed to be isothermal. The positive pressure zone is established using Reynolds boundary condition through iteratively. The various performance parameters which include static, dynamic and stability terms of worn journal bearing are presented with respect to relative wear depth. The journal centre motion trajectories are also obtained by numerically integrated linear and non-linear equation of motion using fourth order Runga-Kutta method. For this a computer program in Mat lab was developed based on analysis to draw the linear and non linear motion trajectories and in order to validate the developed program, the numerically simulated results computed from the present study are compared with the already published results in literature. For analysis purpose the initial values of velocities and displacement are taken as {\bar {\dot X}}\, = \,{\bar {\dot Z}}\, = \,0.0 and {\bar x} and {\bar z}\, = \,0.005 . The results help in predicting bearing life for smooth operation.

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32

Shao, Kang, Chang Wen Liu, Feng Rong Bi, Xia Wang, and Jian Zhang. "Non-Linear Unstability Model and Analysis of the Engine Main Journal Bearing." Applied Mechanics and Materials 246-247 (December 2012): 790–94. http://dx.doi.org/10.4028/www.scientific.net/amm.246-247.790.

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On the base of Reynolds equation, the dynamic load of an engine crankshaft main journal bearing system is studied. The oil film pressure is solved from the non-Newtonian Reynolds equation with non-linear model of a finite length journal bearing. The flexible crankshaft is coupling with hydrodynamic lubrication of bearing film. The elastohydrodynamic bearing is treated as non-linear bearing with the finite difference method when considered the unstability load that was acted on the main journal. This paper aims to identify the non-linear effect of engine main bearing in the case of unstability load.

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33

Chalko, Tom J., and Dong-Xu Li. "Estimation of Alignment and Transverse Load in Multi-Bearing Rotor System." International Journal of Rotating Machinery 3, no. 1 (1997): 11–20. http://dx.doi.org/10.1155/s1023621x9700002x.

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The paper presents a method for estimation of a multi-bearing machine alignment on the basis of measured eccentricities of the shaft in machine bearings. The method uses a linear FEM model of the rotor and the non-linear models of machine bearings. In the presented example, the non-linear models of hydrodynamic bearings are used, but it is shown, that the method could be easily applied to other types of bearings. In addition to the alignment estimation, the method allows to estimate the unknown static load in the transverse direction, reduced to the equivalent load at one or two selected nodes on the shaft. Verification of the method is presented using the model of a machine with vertical shaft supported in three pressurised hydrodynamic bearings. The method is suitable for monitoring of alignment and transverse load during the machine operation.

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34

Schwarzl, Richard, and Roland Netz. "Hydrodynamic Shear Effects on Grafted and Non-Grafted Collapsed Polymers." Polymers 10, no. 8 (August 18, 2018): 926. http://dx.doi.org/10.3390/polym10080926.

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We study collapsed homo-polymeric molecules under linear shear flow conditions using hydrodynamic Brownian dynamics simulations. Tensile force profiles and the shear-rate-dependent globular-coil transition for grafted and non-grafted chains are investigated to shine light on the different unfolding mechanisms. The scaling of the critical shear rate, at which the globular-coil transition takes place, with the monomer number is inverse for the grafted and non-grafted scenarios. This implicates that for the grafted scenario, larger chains have a decreased critical shear rate, while for the non-grafted scenario higher shear rates are needed in order to unfold larger chains. Protrusions govern the unfolding transition of non-grafted polymers, while for grafted polymers, the maximal tension appears at the grafted end.

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35

Heras, Pilar, Sarah Thomas, Morten Kramer, and Jens Peter Kofoed. "Numerical and Experimental Modelling of a Wave Energy Converter Pitching in Close Proximity to a Fixed Structure." Journal of Marine Science and Engineering 7, no. 7 (July 13, 2019): 218. http://dx.doi.org/10.3390/jmse7070218.

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Free-floating bodies are commonly modelled using Cummins’ equation based on linear potential flow theory and including non-linear forces when necessary. In this paper, this methodology is applied to a body pitching around a fixed hinge (not free-floating) located close to a second bottom-fixed body. Due to the configuration of the setup, strong hydrodynamic interactions occur between the two bodies. An investigation is made into which non-linear forces need to be included in the model in order to accurately represent reality without losing computational efficiency. The non-linear forces investigated include hydrostatic restoring stiffness and different formulations of excitation forces and quadratic drag forces. Based on a numerical comparison, it is concluded that the different non-linear forces, except for the quadratic drag force, have a minor influence on the calculated motion of the pitching body. Two formulations of the quadratic drag force are shown to result in similar motions, hence the most efficient one is preferred. Comparisons to wave basin experiments show that this model is, to a large extent, representative of reality. At the wave periods where the hydrodynamic interactions between the bodies are largest, however, the amplitudes of motion measured in the wave basin are lower than those calculated numerically.

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36

Liew, A., N. S. Feng, and E. J. Hahn. "A non-linear transfer matrix technique for statically indeterminate rotor bearing systems." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 215, no. 11 (November 1, 2001): 1343–55. http://dx.doi.org/10.1243/0954406011524720.

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Transfer matrix (TM) methods have long been used to obtain the vibration behaviour of linearized rotor bearing systems. Recently the technique has been enhanced to find the unbalance response of statically determinate systems with hydrodynamic bearing type non-linearities. This paper further extends the non-linear approach to statically indeterminate systems, enabling application to practical rotating machinery. The technique is illustrated on simple unbalanced rotor bearing systems with two and four bearings. It is shown that, in statically indeterminate systems, unbalance may affect not only the orbit size and shape but also the load distribution between the bearings.

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37

Amamou, A., and M. Chouchane. "Non-linear stability analysis of floating ring bearings using Hopf bifurcation theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 12 (July 25, 2011): 2804–18. http://dx.doi.org/10.1177/0954406211413520.

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Floating ring bearings are used to support and guide rotors in several high-speed rotating machinery applications. They are usually credited for lower heat generation and higher vibration suppressing ability. Similar to conventional hydrodynamic bearings, floating ring bearings may exhibit unstable behaviour above a certain stability critical speed. Linear stability analysis is usually applied to predict the stability threshold speed. Non-linear stability analysis, however, is needed to predict the presence and the size of stable limit cycles above the stability threshold speed or unstable limit cycles below the stability critical speed. The prediction of limit cycles is an important step in bearing stability analysis. In this article, a non-linear dynamic model is derived and used to investigate the stability of a perfectly balanced symmetric rigid rotor supported by two identical floating ring bearings near the critical stability boundaries. The fluid film hydrodynamic reactions of the floating ring bearings are modelled by applying the short bearing theory and the half Sommerfeld solution. Hopf bifurcation theory is then utilized to determine the existence and the approximate size of stable and unstable limit cycles in the neighbourhood of the stability critical speed depending on the bearing design parameters. Numerical integration of the non-linear equations of motion is then carried out in order to compare the trajectories obtained by numerical integration to those obtained analytically using Hopf bifurcation analysis. Stability boundary curves for typical bearing design parameters have been decomposed into boundaries with supercritical stable limit cycles and boundaries with subcritical unstable limit cycles. The shape and size of the limit cycles for selected bearing parameters are presented using both analytical and numerical approaches. This article shows that floating ring stability boundaries may exhibit either stable supercritical limit cycles or unstable subcritical limit cycles predictable by Hopf bifurcation.

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38

Vaes, G., and J. Berlamont. "Modelling of overflow emissions in flanders." Water Science and Technology 38, no. 10 (November 1, 1998): 41–48. http://dx.doi.org/10.2166/wst.1998.0373.

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Ideally, for emission calculations long term hydrodynamic simulations should be performed, but this requires long calculation times. Simplifications are consequently necessary. Due to the non-linear behaviour of sewer systems, hydrodynamic simulations using single storm events often will not lead to a good probability estimation of the overflow emissions. Simplified models using long time simulations give better results if they are well calibrated. To increase the accuracy hydrodynamic simulations with short time series can be used. The short time series are selected from the long time historical rainfall series using a simplified model. To test the accuracy of these three methods, hydrodynamic long term simulations were performed for several (small) sewer systems with different characteristics to compare with.

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39

Boyadjiev, Christo, and Maria Doichinova. "A method for stability analysis of the non-linear heat and mass transfer processes." Thermal Science 8, no. 1 (2004): 95–105. http://dx.doi.org/10.2298/tsci0401095b.

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Many systems with non-linear heat and mass transfer processes might be unstable at certain conditions. Small disturbances might bring out them of their equilibrium state, after which they achieve itself to a new stable state. The method developed here concerns a non-linear analysis of hydrodynamic stability of the systems with intensive heat and mass transfer. It al lows the determination of the kinetic energy distribution between the main flow and the disturbance, when the equilibrium value of the disturbance amplitude is determined.

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40

Suarez, Leandro, Rodrigo Cienfuegos, Eric Barthélemy, Hervé Michallet, and Cristian Escauriaza. "LAGRANGIAN DRIFTER MODELLING OF AN EXPERIMENTAL RIP CURRENT." Coastal Engineering Proceedings 1, no. 33 (October 25, 2012): 35. http://dx.doi.org/10.9753/icce.v33.currents.35.

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A non-uniform alongshore wave forcing on an experimental uneven mobile bathymetry create mean circulation on a rip channel. A 2D numerical hydrodynamic model that integrates the non-linear shallow-water equations in a shock-capturing finite-volume framework is used to validate the nearshore circulation, and drifters displacement.

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41

Xiong, Da Run. "Stellar Convection." Publications of the Astronomical Society of Australia 9, no. 1 (1991): 26–31. http://dx.doi.org/10.1017/s1323358000024802.

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AbstractTime-dependent convection theory and non-local convection theory are described. The difference between the convection theories results from the different treatment of the non-linear terms of the hydrodynamic equations. We have obtained a better understanding of the thermodynamic coupling between convection and oscillations in comparison to the dynamic coupling.

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42

Pochai, Nopparat. "A numerical computation of the non-dimensional form of a non-linear hydrodynamic model in a uniform reservoir." Nonlinear Analysis: Hybrid Systems 3, no. 4 (November 2009): 463–66. http://dx.doi.org/10.1016/j.nahs.2009.03.005.

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43

Kirova, N., and S. Brazovskii. "Hydrodynamic theory of plastic flows with conversion." Journal de Physique IV 12, no. 9 (November 2002): 173–76. http://dx.doi.org/10.1051/jp4:20020387.

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Experimental studies show that the sliding state is essentially inhomogeneous with different effects near contacts, in the bulk or at obstacles. We present a general scheme to approach the space - time evolution of deformations, electric fields and currents with particular emphasize t o the current conversion process in Charge Density Waves. We derive general equations for the multifluid hydrodynamics of plastic flows which allow, in principle, to study the transformation of injected carriers from normal electrons to new periods, collective motion in constrained geometry as well as the plastic contribution to non-linear current-voltage characteristics.

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44

Linton, C. M., and D. V. Evans. "Hydrodynamic characteristics of bodies in channels." Journal of Fluid Mechanics 252 (July 1993): 647–66. http://dx.doi.org/10.1017/s0022112093003921.

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The effect of channel walls on the hydrodynamic characteristics of fixed or oscillating bodies is discussed using classical linear water wave theory. Particular attention is paid to the occurrence of trapped modes persisting local to the fixed body and which are manifested in a non-uniqueness of the corresponding forced problem at the trapped mode frequency. The general ideas are illustrated by consideration of two simple geometries for which semi-analytic solutions are available, namely a circular cylinder either partly immersed or extending throughout the water depth, and a thin vertical plate parallel to the channel walls which extends throughout the water depth. Conclusions are drawn concerning the conditions under which trapped modes may exist and their effect on the hydrodynamic characteristics of more general bodies.

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45

Inoue, Yoshiyuki, and Masaki Matsunaga. "Experimental Studies on the Non-linear Hydrodynamic Forces Acting on Bodies Oscillating in Low Frequencies." Journal of the Society of Naval Architects of Japan 1986, no. 160 (1986): 141–51. http://dx.doi.org/10.2534/jjasnaoe1968.1986.160_141.

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46

Chiarelli, Piero. "The Quantum Hydrodynamic Formulation of Dirac Equation and Its Generalized Stochastic and Non-linear Analogs." Physical Science International Journal 5, no. 2 (January 10, 2015): 93–114. http://dx.doi.org/10.9734/psij/2015/12534.

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47

Wu, G. X. "A note on non-linear hydrodynamic forces on a body submerged below a free surface." Applied Ocean Research 15, no. 6 (January 1993): 371–72. http://dx.doi.org/10.1016/0141-1187(93)90005-i.

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48

van der Lee, Loni, Blake Chandrasekaran, Ian Hulme, and Apostolos Kantzas. "A Non-Invasive Hydrodynamic Study of Gas-Solid Fluidised Bed of Linear Low Density Polyethylene." Canadian Journal of Chemical Engineering 83, no. 1 (May 19, 2008): 119–26. http://dx.doi.org/10.1002/cjce.5450830120.

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49

Trebi-Ollennu, A., and B. A. White. "Non-Linear Robust Control Designs for a Remotely Operated Underwater Vehicle Depth Control System." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 210, no. 3 (August 1996): 201–14. http://dx.doi.org/10.1243/pime_proc_1996_210_455_02.

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This paper describes the heave and pitch control of a non-linear longitudinal model of a remotely operated vehicle (ROV) using three robust non-linear control techniques. The techniques are based on input-output (I/O) linearization, comprising basic I/O linearization control, I/O linearization with sliding mode control and I/O linearization with adaptive fuzzy systems. Robustness of the designs is investigated by examining the closed-loop zero dynamics, which are shown to be bounded. The robustness of each control scheme is also investigated by varying the ROV hydrodynamic coefficients by 50 per cent. Simulation results are presented to compare the control schemes.

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50

Raveendran, Vishnu, Emilio Cirillo, and Adrian Muntean. "Upscaling of a reaction-diffusion-convection problem with exploding non-linear drift." Quarterly of Applied Mathematics 80, no. 4 (May 18, 2022): 641–67. http://dx.doi.org/10.1090/qam/1622.

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We study a reaction-diffusion-convection problem with non-linear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. Because of the imposed large drift scaling, this non-linearity is expected to explode in the limit of a vanishing scaling parameter. As main working techniques, we employ two-scale formal homogenization asymptotics with drift to derive the corresponding upscaled model equations as well as the structure of the effective transport tensors. Finally, we use Schauder’s fixed point theorem as well as monotonicity arguments to study the weak solvability of the upscaled model posed in an unbounded domain. This study wants to contribute with theoretical understanding needed when designing thin composite materials that are resistant to high velocity impacts.

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